There are n memory blocks, and the size of the ith block is given by the array memoryBlocks[i], where 0 ≤ i < n.

The following operation can be performed on memoryBlocks one time:

• Select an index x.
• Increase memoryBlocks[x] by 1, but only if memoryBlocks[x] < n - 1.

The smallest integer k not present in memoryBlocks after any number of operations is called a Valid Size, or the MEX (Minimum Excluded Value).

Your task is to return an array of all possible Valid Sizes that can be achieved using memoryBlocks, sorted in increasing order.

Note

The MEX of an array is the smallest non-negative integer that does not appear in the array.

Example

n = 3
memoryBlocks = [0, 3, 4]

If no operation is performed, the Valid Size is 1.

If x = 0, increase memoryBlocks[0] by 1, then the Valid Size is 0.

There are only two possible Valid Sizes.

Output:

[0, 1]

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Function Description

Complete the function

findValidSizes(memoryBlocks)

Parameters

int memoryBlocks[n]

Returns

int[]:
all possible Valid Sizes that can be obtained using memoryBlocks,
sorted in ascending order.

Constraints

1 ≤ n ≤ 10^5
0 ≤ memoryBlocks[i] < n

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Sample Input 0

3
0
2
2

memoryBlocks = [0,2,2]

Sample Output 0

0
1

Explanation

Without any operation,

MEX = 1

Increase

memoryBlocks[0]

by 1.

Array becomes

[1,2,2]

Now

MEX = 0

Hence the answer is

[0,1]

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Sample Input 1

3
2
2
2

memoryBlocks = [2,2,2]

Sample Output 1

0

Explanation

Initially,

MEX = 0

No sequence of operations can make MEX equal to 1 or higher.

Hence the only possible Valid Size is

0

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